Answer
Converges by Alternating Series Test
Work Step by Step
Rewrite the summation, $\Sigma^{\infty}_{n=1} (-1)^{n+1} \frac{1}{n+1}$
Applying the test to see if it meets two conditions
1.) $a_{n+1} \leq a_n$, because $\frac{1}{n+2} \leq \frac{1}{n+1}$
2.)$ \lim\limits_{n \to \infty} \frac{1}{n+1} = 0$
It meets both conditions and the series converges.
